18 Jul 2013

Sum of Diagonals: Upper Secondary Mathematics Competition Question


The figure ABC is a right-angled triangle with lengths AB = AC = 4. Point A1 is the mid-point of the line AC; the point A2 is the mid-point of the line segment A1C, and so on. The line segment A1B1 is perpendicular to AC and intersects the line BC at point B1; similarly A2B2 is perpendicular to AC and intersects BC at B2, and so on.

This construction gives us the diagonal line segments of lengths BA1, B1A2, B2A3 and so on. Calculate the sum of the infinite series

D = BA1 + B1A2 + B2A3 + B3A4 + ...

Hence, if H is the length BC, find the value of D/H.




Feel free to comment, ask questions and even check your answer in the comments box below powered by Disqus Google+.

If you enjoy using this website then please consider making a donation - every little helps :-)

You can receive these questions directly to your email box or read them in an RSS reader. Subscribe using the links on the right.

Don’t forget to follow Gifted Mathematics on Google+Facebook or Twitter. You may add your own interesting questions on our Google+ Community and Facebook..

You can also subscribe to our Bookmarks on StumbleUpon and Pinterest. Many resources never make it onto the pages of Gifted Mathematics but are stored in these bookmarking websites to share with you.


Related Posts Plugin for WordPress, Blogger...